A modified partially averaged Navier–Stokes model (MPANS) is proposed by treating the standard k–ε model as the parent model and formulating the unresolved-to-total kinetic energy ratio fk as a function of the local grid size and turbulence length scale. Flows over a backward facing step are used to evaluate the performance of MPANS mode. Computations of the standard k–ε model, the constant fk partially averaged Navier–Stokes (PANS) models (fk = 0.6, 0.7), and the two-stage PANS model are carried out for comparisons. Based on the detailed analyses of calculated results and experimental data, the MPANS model performs better to predict the reattachment length together with the corner vortex and provides overall improved statistics of skin frictions, pressures, velocity profiles, and Reynolds stresses, demonstrating its promising applications in industrial turbomachines that often encounter with flow separations.

References

1.
Bradshaw
,
P.
, and
Wong
,
F. Y. F.
,
1972
, “
The Reattachment and Relaxation of a Turbulent Shear Layer
,”
J. Fluid Mech.
,
52
(
01
), pp.
113
135
.
2.
Eaton
,
J. K.
, and
Johnston
,
J. P.
,
1981
, “
A Review of Research on Subsonic Turbulent Flow Reattachment
,”
AIAA J.
,
19
(
9
), pp.
1093
1100
.
3.
Driver
,
D. M.
, and
Seegmiller
,
H. L.
,
1985
, “
Features of a Reattaching Turbulent Shear Layer in Divergent Channel Flow
,”
AIAA J.
,
23
(
2
), pp.
163
171
.
4.
Le
,
H.
,
Moin
,
P.
, and
Kim
,
J.
,
1997
, “
Direct Numerical Simulation of Turbulent Flow Over a Backward-Facing Step
,”
J. Fluid Mech.
,
330
, pp.
349
374
.
5.
Kim
,
J. Y.
,
Ghajar
,
A. J.
,
Tang
,
C.
, and
Foutch
,
G. L.
,
2005
, “
Comparison of Near-Wall Treatment Methods for High Reynolds Number Backward-Facing Step Flow
,”
Int. J Comput. Fluid D.
,
19
(
7
), pp.
493
500
.
6.
Šarić
,
S.
,
Jakirlić
,
S.
, and
Tropea
,
C.
,
2005
, “
A Periodically Perturbed Backward-Facing Step Flow by Means of LES, DES and T-RANS: An Example of Flow Separation Control
,”
ASME J. Fluids Eng.
,
127
(
5
), pp.
879
887
.
7.
Yang
,
X. D.
,
Ma
,
H. Y.
, and
Huang
,
Y. N.
,
2005
, “
Prediction of Homogeneous Shear Flow and a Backward-Facing Step Flow With Some Linear and Non-Linear k–ε Turbulence Models
,”
Commun. Nonlinear Sci.
,
10
(
3
), pp.
315
328
.
8.
Erturk
,
E.
,
2008
, “
Numerical Solutions of 2-D Steady Incompressible Flow Over a Backward-Facing Step—Part I: High Reynolds Number Solutions
,”
Comput. Fluids
,
37
(
6
), pp.
633
655
.
9.
Huang
,
B. A.
, and
Wang
,
G. Y.
,
2011
, “
Partially Averaged Navier-Stokes Method for Time-Dependent Turbulent Cavitating Flows
,”
J Hydrodyn.
,
23
(
1
), pp.
26
33
.
10.
Luo
,
X.
,
Huang
,
R.
, and
Ji
,
B.
,
2016
, “
Transient Cavitating Vortical Flows Around a Hydrofoil Using k-ω Partially Averaged Navier–Stokes Model
,”
Mod. Phys. Lett. B
,
30
(
01
), p.
1550262
.
11.
Speziale
,
C. G.
,
1997
, “
Computing Non-Equilibrium Turbulent Flows With Time-Dependent RANS and VLES
,”
Fifteenth International Conference on Numerical Methods in Fluid Dynamics
, Monterey, CA, June 24–28, pp.
123
129
.
12.
Travin
,
A.
,
Shur
,
M.
,
Strelets
,
M.
, and
Spalart
,
P.
,
2000
, “
Detached-Eddy Simulations Past a Circular Cylinder
,”
Flow, Turbul. Combust.
,
63
(
1–4
), pp.
293
313
.
13.
Girimaji
,
S. S.
,
2006
, “
Partially-Averaged Navier-Stokes Model for Turbulence: A Reynolds-Averaged Navier-Stokes to Direct Numerical Simulation Bridging Method
,”
ASME J. Appl. Mech.
,
73
(
3
), pp.
413
421
.
14.
Lakshmipathy
,
S.
, and
Girimaji
,
S. S.
,
2010
, “
Partially Averaged Navier–Stokes (PANS) Method for Turbulence Simulations: Flow Past a Circular Cylinder
,”
ASME J. Fluids Eng.
,
132
(
12
), p.
121202
.
15.
Jeong
,
E.
, and
Girimaji
,
S. S.
,
2010
, “
Partially Averaged Navier–Stokes (PANS) Method for Turbulence Simulations—Flow Past a Square Cylinder
,”
ASME J. Fluids Eng.
,
132
(
12
), p.
121203
.
16.
Song
,
C.-S.
, and
Park
,
S.-O.
,
2009
, “
Numerical Simulation of Flow Past a Square Cylinder Using Partially-Averaged Navier–Stokes Model
,”
J. Wind Eng. Ind. Aerodyn.
,
97
(
1
), pp.
37
47
.
17.
Luo
,
D.
,
Yan
,
C.
, and
Wang
,
X.
,
2015
, “
Computational Study of Supersonic Turbulent-Separated Flows Using Partially Averaged Navier-Stokes Method
,”
Acta Astronaut.
,
107
, pp.
234
246
.
18.
Ji
,
B.
,
Luo
,
X. W.
,
Wu
,
Y. L.
, and
Xu
,
H. Y.
,
2012
, “
Unsteady Cavitating Flow Around a Hydrofoil Simulated Using the Partially-Averaged Navier-Stokes Model
,”
Chin. Phys. Lett.
,
29
(
7
), p.
5
.
19.
Liu
,
J. T.
,
Zuo
,
Z. G.
,
Wu
,
Y. L.
,
Zhuang
,
B. T.
, and
Wang
,
L. Q.
,
2014
, “
A Nonlinear Partially-Averaged Navier-Stokes Model for Turbulence
,”
Comput. Fluids
,
102
, pp.
32
40
.
20.
Frendi
,
A.
,
Tosh
,
A.
, and
Girimaji
,
S.
,
2006
, “
Flow Past a Backward-Facing Step: Comparison of PANS, DES and URANS Results With Experiments
,”
Int. J. Comput. Methods Eng. Sci. Mech.
,
8
(
1
), pp.
23
38
.
21.
Ma
,
J. M.
,
Peng
,
S. H.
,
Davidson
,
L.
, and
Wang
,
F. J.
,
2011
, “
A Low Reynolds Number Variant of Partially-Averaged Navier–Stokes Model for Turbulence
,”
Int. J. Heat Fluid Flow
,
32
(
3
), pp.
652
669
.
22.
Davidson
,
L.
,
2014
, “
The PANS k–ε Model in a Zonal Hybrid RANS–LES Formulation
,”
Int. J. Heat Fluid Flow
,
46
, pp.
112
126
.
23.
Foroutan
,
H.
, and
Yavuzkurt
,
S.
,
2014
, “
A Partially-Averaged Navier–Stokes Model for the Simulation of Turbulent Swirling Flow With Vortex Breakdown
,”
Int. J. Heat Fluid Flow
,
50
(
0
), pp.
402
416
.
24.
Hu
,
C. L.
,
Wang
,
G. Y.
,
Chen
,
G. H.
, and
Huang
,
B.
,
2014
, “
A Modified PANS Model for Computations of Unsteady Turbulence Cavitating Flows
,”
Sci. China-Phys. Mech. Astron.
,
57
(
10
), pp.
1967
1976
.
25.
Girimaji
,
S. S.
, and
Abdol-Hamid
,
K. S.
,
2005
, “
Partially Averaged Navier–Stokes Model for Turbulence: Implementation and Validation
,”
AIAA
Paper No. AIAA 2005-502.
26.
Abdol-Hamid
,
K. S.
, and
Girimaji
,
S. S.
,
2004
, “
A Two-Stage Procedure Toward the Efficient Implementation of PANS and Other Hybrid Turbulence Models
,”
NASA
Technical Report No. TM, 213260.
You do not currently have access to this content.